Precalculus Examples

$\log_{a} (\frac{x^{6}}{y z^{7}})$

Step 1

Rewrite $\log_{a} (\frac{x^{6}}{y z^{7}})$ as $\log_{a} (x^{6}) - \log_{a} (y z^{7})$ .

$\log_{a} (x^{6}) - \log_{a} (y z^{7})$

Step 2

Expand $\log_{a} (x^{6})$ by moving $6$ outside the logarithm.

$6 \log_{a} (x) - \log_{a} (y z^{7})$

Step 3

Rewrite $\log_{a} (y z^{7})$ as $\log_{a} (y) + \log_{a} (z^{7})$ .

$6 \log_{a} (x) - (\log_{a} (y) + \log_{a} (z^{7}))$

Step 4

Expand $\log_{a} (z^{7})$ by moving $7$ outside the logarithm.

$6 \log_{a} (x) - (\log_{a} (y) + 7 \log_{a} (z))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$6 \log_{a} (x) - \log_{a} (y) - (7 \log_{a} (z))$

Step 5.2

Multiply $7$ by $- 1$ .

$6 \log_{a} (x) - \log_{a} (y) - 7 \log_{a} (z)$